Question

Consider the reaction \( \text{CO}(g) + \frac{1}{2} \text{O}_2(g) \longrightarrow \text{CO}_2(g) \).
The value of \( \Delta U \) for the reaction at 300 K is -281.8 kJ mol\(^{-1}\). The value of \( \Delta H \) at same temperature is ......... kJ mol\(^{-1}\). 
[R = 8.3 J K\(^{-1}\) mol\(^{-1}\)] 
 

Hint:

When calculating \( \Delta H \) from \( \Delta U \), remember to include the contribution from the change in the number of moles of gas.

Answer 1

Correct Answer: -282 - -286

Step 1: Understanding the relationship between \( \Delta H \) and \( \Delta U \).
The change in enthalpy \( \Delta H \) and the change in internal energy \( \Delta U \) are related by the equation: \[ \Delta H = \Delta U + \Delta n_g R T \] where \( \Delta n_g \) is the change in the number of moles of gas, \( R \) is the gas constant, and \( T \) is the temperature in Kelvin.

Step 2: Calculating \( \Delta n_g \).
For the given reaction, the change in the number of moles of gas is: \[ \Delta n_g = (1 \, \text{mol of CO}_2) - (1 \, \text{mol of CO} + 0.5 \, \text{mol of O}_2) = 0.5 \]

Step 3: Substituting the values.
Substitute the values into the equation: \[ \Delta H = -281.8 \, \text{kJ/mol} + 0.5 \times 8.3 \times 300 = -282.0 \, \text{kJ/mol} \]

Step 4: Conclusion.
The value of \( \Delta H \) is -282.0 kJ/mol.